Managing temporal cycles in planning problems requiring concurrency

Abstract

To correctly model certain real-world planning problems, it is essential to take into account time. This is the case for problems requiring the concurrent execution of actions (known as temporally expressive problems). In this paper, we define and study the notion of temporally cyclic problems, that is problems involving sets of cyclically dependent actions. We characterize those temporal planning languages, which can express temporally cyclic problems. We also present a polynomial-time algorithm, which transforms a temporally cyclic problem into an equivalent acyclic problem. Applying our transformation allows any temporal planner to solve temporally cyclic problems without explicitly managing cyclicity. We first present our results for temporal PDDL (Planning Domain Description Language) 2.1 and then extend them to a language that allows conditions over arbitrary intervals and effects at arbitrary instants.